The French centre-back, who measures in at a whopping 6 foot 5, played a pivotal role in the Black Cats fending off relegation under Sam Allardyce last season.
But he could already be on his way out of the Stadium of Light, with recent reports claiming the former Lorient star is on Merseyside to push through a summer transfer to Everton following an £18million bid.
The Toffees are eyeing Kone as a direct replacement for John Stones, who completed a £47.5million move to Manchester City on Tuesday.
But the latest reports from The Daily Mail suggest the Goodison outfit could soon be gazumped in the race for the Sunderland defender’s signature by Chelsea.
The Blues consider Kone as a potential alternative to Napoli centre-back Kalidou Koulibaly, after seeing a £42million bid rejected by the San Siro side.
The west London club are also considering Benfica defender Victor Lindelof, whose contract includes a £25million release clause.